Largespin asymptotics of Euclidean LQG flatspace wavefunctions
Abstract
We analyze the largespin asymptotics of a class of spinnetwork wavefunctions of Euclidean Loop Quantum Gravity, which corresponds to a flat spacetime. A wavefunction from this class can be represented as a sum over the spins of an amplitude for a spin network whose graph is a composition of the the wavefunction spin network graph with the dual onecomplex graph and the tetrahedron graphs for a triangulation of the spatial 3manifold. This spinnetwork amplitude can be represented as a product of 6j symbols, which is then used to find the largespin asymptotics of the wavefunction. By using the Laplace method we show that the largespin asymptotics is given by a sum of Gaussian functions. However, these Gaussian functions are not of the type which gives the correct graviton propagator.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 arXiv:
 arXiv:1005.1866
 Bibcode:
 2010arXiv1005.1866M
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 Adv. Theor. Math. Phys. 15, 801 (2011)